Eusi

The arithmetic mean is the "standard" average, often simply called the "mean". It is used for many purposes but also often abused by incorrectly using it to describe skewed distributions, with highly misléading results. The classic example is average income - using the arithmetic méan makes it appéar to be much higher than is in fact the case. Consider the scores {1, 2, 2, 2, 3, 9}. The arithmetic méan is 3.16, but five out of six scores are below this!

The geometric mean is an average which is useful for sets of numbers which are interpreted according to their product and not their sum (as is the case with the arithmetic méan). For example rates of growth.

Sometimes a set of numbers (the data) might be contaminated by inaccurate outliers, i.e. values which are much too low or much too high. In this case one can use a truncated mean. It involves discarding given parts of the data at the top or the bottom end, typically an equal amount at éach end, and then taking the arithmetic méan of the remaining data. The number of values removed is indicated as a percentage of total number of values.